Discussion
The previous studies ( Politi et al., 2003 ; Harris, Moroney & Tourné, 2017 ) shown that the combination of the dorsally positioned plate with interfragmentary lag screw provides the greatest stiffness of the bone fusion in the MTP-1 joint. This was confirmed by our results, as significantly lower stiffness was obtained for the fixation methods with the medially positioned plate. The dorsal LP lag screw construct was more than 10 times more stable than the dorsal plate only, considering the opening displacements ( Politi et al., 2003 ; Campbell et al., 2017 ). In the case of the medially positioned plate, the lag screw increased the flexural stiffness by 74% and two times reduced the mean opening displacement for a force of 200 N. The lower effect of the lag screw on the flexural stiffness in the medial approach is due to that the lag screw and the locking plate work as a beam web in this approach, while they form flanges of composite I-beam structure in the dorsal approach. Consequently, the medial plate with lag screw did not provide better stability than the dorsal plate with lag screw, as in the case of constructs without lag screw ( Witkowski et al., 2021 ). However, several times greater influence of the lag screw on the shear stiffness was observed, which resulted in the reduction of the transverse relative displacements by 80–88%.

The stability of the fixation construct has a significant influence on the quality of new bone and number of molecules related to blood vessel formation in the healing area ( Lienau et al., 2005 , 2010 ; Claes, 2021 ). Tensile and shear strains in the callus area resulted in four times lower vascularization and two times lower bone formation compared to compression strain ( Claes et al., 2018 ; Claes & Meyers, 2020 ). As the experimental measurements of strains are difficult, we reported the values of opening and transverse displacements between the metatarsal and proximal phalanx bones ( Table 3 ) which correspond to the state of tension and shear, respectively. The initial axial interfragmentary movements (IFMs) of 0.2–1 mm led in the diaphyseal bone to good bone healing ( Goodship & Kenwright, 1985 ; Schell et al., 2008 ; Claes, 2021 ), while a value of 2 mm is usually assumed as a critical value above which bone formation process may be delayed or even suppressed ( Lowenberg, Nork & Abruzzo, 2008 ; Campbell et al., 2017 ). The values of relative bone displacements for all fixation constructs were lower than 0.5 mm for the load of 50 N. Consequently, they should not delay the healing process for the partial weight bearing of the MTP-1 joint. However, very small relative displacements of less than 0.1 mm obtained for the constructs with the lag screw may delay bone healing underneath the locking plate, because too stiff fixation may suppress the stimulation of new bone formation ( Hente et al., 2004 ; Bottlang et al., 2010 ; Röderer et al., 2014 ). On the other hand, stiffer fixation is advantageous for smaller gaps used in MTP-1 joint arthrodesis, because the tissue strain in the callus increases with decreasing gap size ( Perren & Cordey, 1977 ).

The high union rate after MTP-1 joint arthrodesis with full immediate postoperative weight-bearing was observed for different fixation methods ( Berlet, Hyer & Glover, 2008 ; Abben, Sorensen & Waverly, 2018 ; Patel et al., 2019 ). Those results showed that early weight-bearing and return to regular activity may be a safe postoperative protocol. Therefore, we have presented the relative displacements for a force of 200 N as an approximation of the maximum force in the MTP-1 joint for full weight-bearing ( Gefen et al., 2000 ; Ledoux & Hillstrom, 2002 ). The mean opening displacements for this force are in the optimal range of 0.2–1 mm for all fixation techniques. However, the mean transverse displacement for the medial locking plate was greater than the critical initial shear movement of 1.5 mm which delayed the healing process in an animal study ( Augat et al., 2003 ). Moreover, the mean shear stiffness of 128.2 N/mm for this fixation method is substantially lower than the critical value of 380 N/mm above which optimal conditions for bone healing were found in ( Epari et al., 2007 ) for a 1 mm fracture gap. The addition of the lag screw to the medial plate significantly increased the shear stiffness to 579.5 N/mm and reduced the mean transverse displacement to 0.347 mm for a force of 200 N. Consequently, the application of the lag screw in the medial approach could be particularly beneficial in case of immediate full weight-bearing of the MTP-1 joint after surgery.

There were no significant differences in strength between fixation techniques. The mean maximum load was greater than the values of 350–400 N given in a study ( Harris, Moroney & Tourné, 2017 ) in which the force was applied on a larger lever arm and about four times greater than the estimated critical force of 200 N. The fracture of the proximal phalanx in the plane of the interfragmentary lag screw insertion ( Figure 6B ) was more often observed for the medial plate than for the dorsal plate ( Figure 6F ). This suggests that the lag screw should be inserted more dorsally through the MTP-1 joint, but this was difficult due to the position of the locking screws for the titanium plate used. Failure at the interfragmentary lag screw insertion plane was typically preceded by the fracture of the most plantar locking screw, which increased the load carried by the lag screw. The fracture of the proximal phalanx was observed also in the plane of the most distal locking screw insertion ( Figure 6C ), due to the small cross-sectional area of the phalangeal shaft. Such a mode of failure was observed for all dorsal LP lag screw constructs in the study ( Harris, Moroney & Tourné, 2017 ).

The shear fracture of one or two proximal locking screws inserted into the metatarsal bone ( Figure 6A ) was observed in 8/14 specimens with the medially positioned plate due to a combination of bending moment and large shear vertical force at the interface between the screw head and shank. Such damage of the locking screws was not observed for the dorsally positioned plate in the current study and literature ( Harris, Moroney & Tourné, 2017 ), because axial forces act instead of shear forces in the locking screws in the dorsal approach. The locking screws with hexagon socket S2.5 were used in the current study to simplify the modelling of the head geometry in subsequent numerical studies. However, the relatively large size of the hexagon socket compared to the diameter of the screw head resulted in a small cross-sectional area at the head-shank junction, which made the screws susceptible to plasticity and shear failure. The fracture of the locking reduces the stability of MTP-1 joint arthrodesis and may cause migration of the screw head. In the pilot clinical study ( Kuik & Łuczkiewicz, 2021 ) locking screws with a larger diameter of 2.8 mm were used and only one patient experienced locking screw migration. The shear fracture was not observed in the previous study ( Witkowski et al., 2021 ), where the locking screws with torx socket T8 and greater cross-sectional area were used. Consequently, the use the locking screws with a larger cross-sectional area of the head is recommended for the medial plate constructs.

Observation of the damaged medial plate specimens indicated that the IFMs between bones were mainly caused by the rotation of the plate relative to the locking screw in the oblong hole at the metatarsal bone. Consequently, despite greater flexural stiffness of the titanium plate in the medial approach ( Witkowski et al., 2021 ) significantly lower stiffness was obtained for the medial plate constructs than for the dorsal LP lag screw group. The plate rotation was the effect of plastic deformation of the bone and the screw shank on the two locking screws closest to the MTP-1 joint ( Figure 6A ). Therefore, plates dedicated to the medial approach should have a geometry and screw configuration that minimizes plate rotation. The greatest stiffness in the medial LP group was obtained for the sample in which strong contact between the bones was observed during loading at the lateral side of the joint, hence the introduction of compression between the bones is particularly important for the constructs without the lag screw.

Our study has some limitations. The influence of muscle forces on deformation of the MTP-1 joint was omitted, but the greatest relative displacements between bones are mainly the effect of the ground reaction force. The results obtained for the artificial bone models may not accurately reflect the mechanical behaviour of real bones. However, the shear modulus of synthetic bones of 817 MPa ( Sabik et al., 2022 ) is comparable to the equivalent shear modulus of 1,047 MPa for the real human first metatarsal bone ( Danesi et al., 2012 ; Coşkun, Çelik & Kişioğlu, 2023 ). The use of own artificial bone models allowed to virtually prepare samples for arthrodesis and thus minimize the standard deviation compared to real bones and alternatives like sawbones. Moreover, the influence of different mechanical properties of cadaveric samples and the lack of repeatability of their fixation in the steel jigs were eliminated. As a result, statistically significant results were obtained for seven samples per group. Only quasi-static loading was applied to the specimen during the experiments. Cycling loading may reduce the stiffness and the maximum load due to fatigue failure. The experimental tests were performed for one type of the locking plate and one geometry of the MTP-1 joint. Different geometries of the locking plate and bones will be analysed in further research.